2018 AMC 12A Problem 22

The solutions to the equations z^2=4+4\sqrt{15}i and z^2=2+2\sqrt 3i, where i=\sqrt{-1}, form the vertices of a parallelogram in the complex plane. The area of this parallelogram can be written in the form p\sqrt q-r\sqrt s, where p, q, r, and s are positive integers and neither q nor s is divisible by the square of any prime number. What is p+q+r+s?

\textbf{(A) } 20 \qquad \textbf{(B) } 21 \qquad \textbf{(C) } 22 \qquad \textbf{(D) } 23 \qquad \textbf{(E) } 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.